Nonlinear potential theory and weighted Sobolev spaces /
The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space the...
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| Auteur principal: | |
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| Format: | Base de données |
| Langue: | English |
| Publié: |
Berlin
Springer
c2000.
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| Collection: | Lecture notes in mathematics (Springer-Verlag) ;
1736. |
| Sujets: | |
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| Résumé: | The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincar inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincar inequalities, and spectral synthesis theorems. |
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| Description matérielle: | 1 CD-ROM 12 cm |
| Bibliographie: | Includes bibliographical references (pages [163]-170) and index. |
| ISBN: | 9783540451686 (electronic bk.) 3540451684 (electronic bk.) |
| ISSN: | 0075-8434 ; |